which is equivalent to (REF ). As anticipated in Remark REF , this equation (see, e.g., the monograph [1]} or the review paper [2]}) defines a Hamiltonian Boundary Value Method with parameters \(k\)  and \(s\) , in short HBVM\((k,s)\). Moreover, also Theorems REF –REF  exactly describe, in the case of problem (REF ), their conservation and accuracy properties. For this reason, the methods here presented can be regarded as a generalization of HBVMs for solving Poisson problems and, therefore, this fact, motivates the following definition.
